Twin Paradox and the Logical Foundation of Relativity Theory

We study the foundation of space-time theory in the framework of first-order logic (FOL). Since the foundation of mathematics has been successfully carried through (via set theory) in FOL, it is not entirely impossible to do the same for space-time theory (or relativity). First we recall a simple and streamlined FOL-axiomatization Specrel of special relativity from the literature. Specrel is complete with respect to questions about inertial motion. Then we ask ourselves whether we can prove the usual relativistic properties of accelerated motion (e.g., clocks in acceleration) in Specrel. As it turns out, this is practically equivalent to asking whether Specrel is strong enough to “handle” (or treat) accelerated observers. We show that there is a mathematical principle called induction (IND) coming from real analysis which needs to be added to Specrel in order to handle situations involving relativistic acceleration. We present an extended version AccRel of Specrel which is strong enough to handle accelerated motion, in particular, accelerated observers. Among others, we show that~the Twin Paradox becomes provable in AccRel, but it is not provable without IND.     

On theK-property of some planar hyperbolic billiards

TheK-property is demonstrated for a class of planar billiards satisfying Wojtkowski's principles. Their boundary may consist of convex-scattering, concave and linear pieces. Earlier Wojtkowski showed that these billards had non-zero Lyapunov exponents.     

Q value related mass determinations using a Penning trap

We report here about measurements of reaction and decay Q values by precise determination of pairs of atomic masses. These were performed with the Penning trap mass spectrometer SMILETRAP. Measurements with Penning traps give reliable and accurate masses, in particular Q values, due to the fact that certain systematic errors to a great deal cancel in the mass difference between the two atoms defining the Q value. Some Q values that are of fundamental interest will be discussed here, for example, a new Q value for the ⁶Li (n,γ) ⁷Li reaction, for the β-decay of tritium, related to properties of the electron neutrino mass, and for the neutrino-less double β-decay of ⁷⁶Ge, related to the question of whether the neutrino is a Majorana particle or not. In case of the latter two we report the most accurate Q values, namely 18,589.8(12) eV for the tritium decay and 2,038.997(46) keV for the neutrino-less double β-decay of ⁷⁶Ge.     

The simulation of molecular and organic devices: a critical review and look at future developments

Molecular devices have lately attracted increased attention due to some appealing features such as their low production cost, flexibility in the substrate choice, possibility of large area deployment, and possibly higher integration capabilities. Starting from a series of results obtained from our groups, we critically review the state-of-the-art in the field of simulation of organic and molecular systems, by analyzing and comparing existing approaches, and looking at the open problems and possible solutions and future developments. PACS 72.80.Le     

Innately transitive subgroups of wreath products in product action

A permutation group is innately transitive if it has a transitive minimal normal subgroup, which is referred to as a plinth. We study the class of finite, innately transitive permutation groups that can be embedded into wreath products in product action. This investigation is carried out by observing that such a wreath product preserves a natural Cartesian decomposition of the underlying set. Previously we classified the possible embeddings in the case where the plinth is simple. Here we extend that classification and identify several different types of Cartesian decompositions that can be preserved by an innately transitive group with a non-abelian plinth. These different types of decompositions lead to different types of embeddings of the acting group into wreath products in product action. We also obtain a full characterisation of embeddings of innately transitive groups with diagonal type into such wreath products.

     

The Choquet-Deny convolution equation μ=μ*σ for probability measures on Abelian semigroups

In this note, we characterize the regular probability measures satisfying the Choquet-Deny convolution equation =* on Abelian topological semigroups for a given probability measure .     

Thermal degradation of copolymers of styrene and methyl-vinyl-silane by pyrolysis gas chromatography

Pyrolysis gas chromatographic investigations have been carried out on copolymers of styrene with trimethyl-vinyl-silane and of styrene with dimethyl-phenyl-vinyl-silane, in order to study the mechansims of thermal degradation and the copolymer structures. We have identified the pyrolysis products and measured their relative amounts. The experiments show that the controlling factor in the mechanism of the degradation is the nature of the side-group attached to the carbon atom at which chain scission occurs. If this side-group is phenyl, the main degradation process is depropagation; if it is if it is trimethyl-silyl or dimethyl-phenyl-silyl, intramolecular hydrogen abstraction followed by β scission becomes more important than depropagation. From the point of view of degradation mechanism, the nature of the side-group attached to the carbon atom from which the hydrogen is abstracted is of minor importance.We estimated the average copolymer block length from the amounts of products containing both comonomers as well as from the amounts of trimer composed of the same monomer.     

Study of fragmentation pattern and adsorption of 9-O-(triphenylsilyl)-10,11-dihydrocinchonidine on platinum by hydrogen/deuterium exchange using electrospray ionization ion-trap tandem mass spectrometry

We have studied the adsorption on a platinum (Pt) catalyst of two compounds utilizable as a chiral basic catalyst and a chiral modifier, dihydrocinchonidine (DHCD), and a new cinchona alkaloid derivative containing a bulky group, the Ph3SiO-DHCD molecule. The method of choice was the detection by electrospray ionization (ESI) ion-trap tandem mass spectrometry (MS/MS) of hydrogen/deuterium (H/D) exchange at room temperature, in tetrahydrofuran, at a D2 pressure of 1 bar. Based on the ESI-MS/MS spectrum of the new compound, we propose a mechanism for the formation of the silatropylium cation containing a Si-O bond. From the fragmentation pattern of Ph3SiO-DHCD it was confirmed that ESI-ion-trap MS/MS can be used to study the adsorption processes of complicated carbon compounds by investigating their H/D exchange reactions. In the case of Ph3SiO-DHCD, the results demonstrate that H/D exchange takes place mainly on the quinoline skeleton. However, the strong pi-bonded adsorption of the quinoline skeleton parallel with the imaginary plane of Pt is not preferred because the bulky Ph3Si group inhibits the multiple pi-bonded adsorption of the Ph3SiO-DHCD. Because of this hindrance the molecule was adsorbed tilted via the nonbonding electron pair of the N atom and C2' atom of the quinoline skeleton; consequently, mainly alkaloid-d1 and alkaloid-d2 are formed.